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An identity involving Nörlund polynomials

Published online by Cambridge University Press:  17 April 2009

A.E. Özlük  and
C. Snyder
A.E. Özlük
Affiliation:
Department of Mathematics, Neville Hall University of Maine Orono, Maine 04469, United States of America
C. Snyder
Affiliation:
Department of Mathematics, Neville Hall University of Maine Orono, Maine 04469, United States of America
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Abstract

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We prove an identity involving Nörlund polynomials, the proof of which is elementary and involves the enumeration of lattice points. The identity is slightly stronger than an identity of Carlitz which he obtained by using Apostol's transformation formula for Lambert series.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 43 , Issue 2 , April 1991 , pp. 307 - 315
Copyright
Copyright © Australian Mathematical Society 1991

References

[1]Apostol, T., ‘Generalized Dedekind sums and transformation formulae of certain Lambert series’, Duke Math. J. 17 (1950), 147–157.CrossRefGoogle Scholar
[2]Carlitz, L., ‘Some theorems on generalized Dedekind sums’, Pacific J. Math. 3 (1953), 513–522.CrossRefGoogle Scholar
[3]Kallies, J., ‘Verallgemeinente Dedekindsche Summen und ein Gitterpunktproblem in n−dimensionalen Raum’, J. Reine Angew. Math. 344 (1983), 22–37.Google Scholar
[4]Nörlund, N.E., Vorlesungen über Differenzrechnung (Berlin, 1924).Google Scholar